A loss on property income cannot usually be set against other income of the same year - it must be carried forward against future property profits. If you received incorrect advice from HMRC (and can prove it), then seeking advice would hopefully be treated as "taking reasonable care". An error "despite taking reasonable care" does not attract a monetary penalty.
You can argue about penalties (both whether one is charged and, if so, the amount) but you cannot contest the interest - there is no right of appeal against interest. It is charged when people pay late - simple as that - with no real notice taken of the reason for late payment. The bottom line is that you have had the money and HMRC has been denied that same money.
Am I allowed to offset the remainder of my tax free allowance against the tax owed or could i only do that if I posted a loss?
I don't understand the question. Your personal allowance is used against taxable income; there is no direct link with a tax liability. Are you saying that you owe £2,500 and if you had £1,000 unused personal allowance could the bill be reduced to £1,500? If that is your question, the answer is "no".
Offering half in full and final settlement will be a non-starter. The tax and interest are almost certainly non-negotiable. Assuming that you have ongoing income and some assets, then HMRC will expect you to pay in full, somehow, eventually. Getting away with paying half is a "man down the pub" story. Or perhaps Vodafone if the rumours are to be believed? It might happen occasionally, but maybe only where it's a "that or nothing" scenario.